Aircraft: MBB-BK 117 ALL SERIES
Phase of flight: Parked
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Maintenance; Deviation / Discrepancy - Procedural Published Material / Policy

My day started at XA:30am to assist with the AAIP (Approved Aircraft Inspection Program) inspection on the back up aircraft. Removed tail rotor blade individually for AAIP Zone 12 section A0312.10.2 inspection. I loosened both attaching bolts; removed one nut/washer; removed bolt; pivoted tail rotor blade away from the mount and reinstalled the bolt and washer/nut; removed other mounting hardware in the same manner to preserve hardware installation location. I took the blade down to a bench to clean and inspect. Reinstalled the inspected blade in the reverse of removal. Repeated the process for the second blade. I was aware the blades are easy to install backwards; but somehow that happened with one of the blades. I had the Lead mechanic look over the work; for installation and cotter pins.The Pilot also looked at the work. All three of us missed that one blade was installed backwards. During the initial run up for track and balance; the Pilot commented how rough the tail rotor pedals felt; I observed the tail area shaking more than normal and told the pilot to shut it down. Only one engine was started and at ground idle. I was thinking at the time that maybe I had dropped a washer during the removal/installation. After shut down; The Lead Mechanic came out asking what was wrong; I told him we had a bad vibration and he noticed the tail rotor blade installed backwardsStarting later in the day today would have allowed for more rest prior to working for me. Due to my assisting with the heavy maintenance on the base aircraft as well as taking care of my base aircraft in [another city]; the past 2 weeks have been full of fairly long days. Having a more thorough RII / CYA; standing back and looking at the big picture and not focusing just on cotter pins being installed. I could have marked the blade before I took it off to help ensure I got it installed correctly as well. We were going to start an A/F zone 12 inspection by completing the tail rotor sections; essentially visually inspect the system; remove the tail rotor blades from hub (hub is still on aircraft) inspect attachment and dynamically balance tail rotor. I left the hangar to run over to the [other company location] to look for some equipment and the base mechanic stayed to remove the tail rotor blades. When I returned he told me he had the blades off and back on and was just finishing the cotter pins. when he was finished I looked at the back side of the blades and verified that cotter pins were installed; the pilot was informed of what was done and she looked it over as well; we pushed the aircraft out to start the balance runs. I went back into the office to work on the paperwork and heard the aircraft start 1 engine and immediately shut down. After shut down it was determined that one tail rotor blade was installed backwards. At that point I looked up the measures to take for high vibrations and contacted my [supervisor].This aircraft is a backup aircraft covering heavy maintenance on our base aircraft. Slow down; since the base has been under stress given the maintenance on primary aircraft and the mechanic had to drive up we should have started the maintenance later in the morning to allow for more rest. Most importantly I should have stood back and looked at the big picture of the blade removal and not focused on the attachment of the blades. Aircraft Mechanic accomplishing routine inspection on BK-117 helicopter installed tail rotor blade incorrectly. Identified problem during post maintenance run-up and corrected problem.